Question: Solve for $q$, $ \dfrac{4q + 4}{4q - 1} = \dfrac{7}{20q - 5} - \dfrac{4}{20q - 5} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4q - 1$ $20q - 5$ and $20q - 5$ The common denominator is $20q - 5$ To get $20q - 5$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{4q + 4}{4q - 1} \times \dfrac{5}{5} = \dfrac{20q + 20}{20q - 5} $ The denominator of the second term is already $20q - 5$ , so we don't need to change it. The denominator of the third term is already $20q - 5$ , so we don't need to change it. This give us: $ \dfrac{20q + 20}{20q - 5} = \dfrac{7}{20q - 5} - \dfrac{4}{20q - 5} $ If we multiply both sides of the equation by $20q - 5$ , we get: $ 20q + 20 = 7 - 4$ $ 20q + 20 = 3$ $ 20q = -17 $ $ q = -\dfrac{17}{20}$